A variety of techniques have been utilized in determining the presence and in estimating quantities of hydrocarbons (oil and gas) in earth formations. These methods are designed to determine formation parameters, including among other things, porosity, fluid content and permeability of the rock formation surrounding the wellbore drilled for recovering hydrocarbon. Typically, the tools designed to provide the desired information are used to log the wellbore. Much of the logging is done after the well bores have been drilled. More recently, wellbores have been logged while drilling of the wellbores, which is referred to as measurement-while-drilling ("MWD") or logging-while-drilling ("LWD"). Measurements have also been made when tripping a drillstring out of a wellbore: this is called measurement-while-tripping ("MWT").
One recently evolving technique involves utilizing Nuclear Magnetic Resonance (NMR) logging tools and methods for determining, among other things porosity, hydrocarbon saturation and permeability of the rock formations. The NMR logging tools are utilized to excite the nuclei of the of the fluids in the geological formations in the vicinity of the wellbore so that certain parameters such as spin density, longitudinal relaxation time (generally referred to in the art as "T.sub.1 ") and transverse relaxation time (generally referred to as "T.sub.2 ") of the geological formations can be estimated. From such measurements, porosity, permeability and hydrocarbon saturation are determined, which provides valuable information about the make-up of the geological formations and the amount of extractable hydrocarbons.
A typical NMR tool generates a static magnetic field B.sub.0 in the vicinity of the wellbore, and an oscillating field B.sub.1 in a direction perpendicular to B.sup.0. This oscillating field is usually applied in the form of short duration pulses. The purpose of the B.sub.0 field is to polarize the magnetic moments of nucleii parallel to the static field and the purpose of the B.sub.1 field is to rotate the magnetic moments by an angle .theta. controlled by the width t.sub.p and the amplitude B.sub.1 of the oscillating pulse. With the variation of the number of pulses, pulse duration and pulse intervals, various pulse sequences can be designed to manipulate the magnetic moment, so that different aspects of the NMR properties can be obtained. For NMR logging, the most common sequence is the Carr-Purcell-Meiboom-Gill ("CPMG") sequence that can be expressed as EQU TW-90-(t-180-t-echo).sub.n
After being tipped by 90.degree., the magnetic moment precesses around the static field at a particular frequency known as the Larmor frequency .omega..sub.0, given by .omega..sub.0 =.gamma.B.sub.0, where B.sub.0 is the field strength of the static magnetic field and .gamma. is the gyromagnetic ratio. At the same time, the single magnetic moments return to the equilibrium direction (i.e., aligned with the static field) according to a decay time known as the "spin-lattice relaxation time" or T.sub.1. Inhomogeneities of the B.sub.0 field result in dephasing of the magnetic moments and to remedy this, a 180.degree. pulse is included in the sequence to refocus the magnetic moments. This gives a sequence of n echo signals.
U.S. Pat. No. 5,023,551 issued to Kleinberg discloses an NMR pulse sequence that has an NMR pulse sequence for use in the borehole environment which combines a modified fast inversion recovery (FIR) pulse sequence with a series of more than ten, and typically hundreds, of CPMG pulses according to EQU [W.sub.i -180-TW.sub.i -90-(t-180-t-echo).sub.j ].sub.1
where j-1,2, . . . J and J is the number of echoes collected in a single Carr-Purcell-Meiboom-Gill (CPMG) sequence, where i=1, . . . I and I is the number of waiting times used in the pulse sequence, where W.sub.i are the recovery times, TW.sub.i are the wait times before a CPMG sequence, and where t is the spacing between the alternating 180.degree. pulses and the echo signals.
Proton NMR measurement is typically performed for logging since hydrogen is abundant in reservoir fluids. T2 is very short in solids, but relatively long in liquids and gases, so that the NMR signal from the solid rock decays quickly and only the signal from fluids in the rock pores in the region of interest is seen. This signal may arise from hydrogen in hydrocarbon or water within the pores of the formation. The local environment of the hydrogen influences the measured T2 or "spin-spin" relaxation. For example, capillary bound fluid has a shorter T2 than fluid in the center of a pore, the so-called "free fluid." In this way, the NMR tool can be used advantageously to distinguish between producible fluid and non-producible fluid.
The NMR echo signals provide information about fluid and rock properties. Depending upon the goal of the investigation, various NMR measurement techniques can be used to obtain different petrophysical properties (e.g., partial and total porosities) or to discern multiphase fluids for hydrocarbon typing purposes. The different NMR acquisition techniques are characterized by differences in pulse timing sequences as well as repetition times between measurements. In addition, in wireline applications, multiple runs of NMR acquisition sequences with different parameters can be combined to enhance the analysis of the desired petrophysical information. However, in measurement-while-drilling applications or in measurement-while-tripping applications, it is not possible to make multiple runs, so that all the desired information must be obtained at one time while the borehole is being drilled or tripped.
Several methods to identify and quantify gas reservoirs have been employed during the last few years utilizing the effect of different wait times on the measured NMR signal. Depending upon the fluid properties, the wait time (TW) determines the amount of the polarized medium that contributes to the measured signal. For example, Akkurt et.al. disclose a Differential Spectrum Method (DSM) based upon this effect in their paper "NMR Logging of Natural Gas Reservoirs" presented at the 36.sup.th Annual Meeting of the Society of Professional and Well Log Analysts (SPWLA) in 1995. Another related technique is the Time Domain Analysis (TDA) presented in the 1995 Society of Petroleum Engineers meeting by Prammer et. al. in a paper entitled "Lithology-Independent Gas Detection by Gradient NMR Logging." These techniques require the calculation of differential echo signals or differential T.sub.2 spectra that are derived from the echo trains by an inversion. The differential quantities are derived from two echo train data acquired with different wait times by subtracting either the echo train data or their T.sub.2 spectra. As would be known to those versed in the art, this subtraction of one noisy signal from a second noisy signal leads to a reduction in signal-to-noise ratio. This, coupled with the low hydrogen density of a gaseous hydrocarbon, is a major problem in accurately estimating reservoir properties.
European Patent Application 0 871 045 of Freedman discloses a method in which an oscillating magnetic field is produced according to the Carr-Purcell-Meiboom-Gill (CPMG) sequence to induce NMR echo signals. The spin echo signals are separated into a first set and a second set wherein the first set comprises the early-time echo signals and the second set comprises the remaining echo signals. The second set of echo signals are subdivided into a plurality of groups and a window sum value is generated for each group of the second set, producing a plurality of window sums.
In formations having a gas saturation, the porosity as determined by a conventional density tool needs to be corrected because the presence of the gas phase causes the porosity to be overestimated. On the other hand, an NMR-derived porosity obtained using a CPMG sequence wherein TW is sufficiently long to substantially polarize all the formation fluid in the sensitive volume underestimates the true porosity. Solving a system of two equations, the true porosity is then obtained as a function of the NMR derived porosity, the density derived porosity, and a hydrogen index of the liquid phase HI.sub.l in the flushed zone at reservoir conditions. EQU .PHI.=wPORZ+(1-w)TPOR/HI.sub.l
where PORZ is the porosity derived from the density measurement, TPOR is the NMR-derived porosity. The value of w depends, among other factors, on the hydrogen index of the gas phase HI.sub.g, the CPMG pulse sequence TW and the longitudinal NMR relaxation time of the gas T.sub.1,g. Freedman suggests that a quick estimate of the porosity can be obtained by using a value of 0.6 for w, and using a value for HI.sub.l of 1.0, so that the true porosity becomes a weighted average of the density derived porosity and NMR derived porosity.
There is a need for a method of obtaining the porosity and gas saturation of a reservoir more accurately and without making the approximation of using a constant weighting factor w. There is also a need to characterize the gas phase by the spin-lattice relaxation time of the gas T.sub.1g, the hydrogen index of the gas HI.sub.g, and density of the gas .rho..sub.g in order to derive the gas saturation S.sub.g,xo of the reservoir. The present invention satisfies this need.